# Print Gallery (M. C. Escher)

* Print Gallery* (Dutch:

*Prentententoonstelling*) is a lithograph printed in 1956 by the Dutch artist M. C. Escher. It depicts a man in a gallery viewing a print of a seaport, and among the buildings in the seaport is the very gallery in which he is standing. The lithograph has attracted discussion in both mathematical and artistic contexts.

## Origins

Bruno Ernst cites M. C. Escher as stating that he began *Print Gallery* "from the idea that it must be possible to make an annular bulge, a cyclic expansion ... without beginning or end."^{[1]} Escher attempted to do this with straight lines, but intuitively switched to using curved lines which make the grid expand greatly as it rotates.^{[1]}^{[2]}

## Seeming paradox

In the book *Gödel, Escher, Bach*, Douglas Hofstadter explains it as a strange loop showing three kinds of "in-ness": the gallery is physically in the town ("inclusion"); the town is artistically in the picture ("depiction"); the picture is mentally in the person ("representation").^{[3]}

## Possible Droste effect

Escher's signature is on a circular void in the center of the work. In 2003, two Dutch mathematicians, Bart de Smit and Hendrik Lenstra, reported a way of filling in the void by treating the work as drawn on an elliptic curve over the field of complex numbers. They deem an idealized version of *Print Gallery* to contain a copy of itself (the Droste effect), rotated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58.^{[2]} Their website further explores the mathematical structure of the picture.^{[4]}

## Post-modernism

*Print Gallery* has been discussed in relation to post-modernism by a number of writers, including Silvio Gaggi,^{[5]} Barbara Freedman,^{[6]} Stephen Bretzius,^{[7]} and Marie-Laure Ryan.^{[8]}

## References

- 1 2 Ernst, Bruno.
*De toverspiegel van M. C. Escher*, Meulenhoff, Amsterdam, 1976; English translation by John E. Brigham:*The Magic Mirror of M. C. Escher*, Ballantine Books, New York, 1976 - 1 2 de Smit, B.; Lenstra, H. W. (2003). "The Mathematical Structure of Escher's Print Gallery".
*Notices of the American Mathematical Society*.**50**(4): 446–451. - ↑ Cooper, Jonathan (5 September 2007). "Art and Mathematics". Retrieved 5 September 2015.
- ↑ Lenstra, Hendrik; De Smit, Bart. "Applying mathematics to Escher's Print Gallery". Leiden University. Retrieved 10 November 2015.
- ↑ Gaggi, Silvio (1989).
*Modern/Postmodern: A Study in Twentieth-Century Arts and Ideas*. University of Pennsulvania Press. pp. 44–45. ISBN 0-8122-8154-3. - ↑ Freedman, Barbara (1991).
*Staging the gaze: postmodernism, psychoanalysis, and Shakespearean comedy*. Cornell University Press. pp. 124–126. ISBN 0-8014-9737-X. - ↑ Bretzius, Stephen (1997).
*Shakespeare in theory: the postmodern academy and the early modern theater*. University of Michigan Press. p. 57. ISBN 0-472-10853-0. - ↑ Ryan, Marie-Laure (2000).
*Narrative as virtual reality: immersion and interactivity in literature and electronic media*. Johns Hopkins University Press. p. 165. ISBN 0-8018-6487-9.

## External links

- HarryCarry5 (Jul 26, 2009).
*Escher's Print Gallery Explained*. YouTube. - Artful Mathematics: The Heritage of M. C. Escher, by Bart de Smit and Hendrik Lenstra
- Escher's prentententoonstelling (Escher's picture gallery) shows an animation of the mathematical transformations involving a 3-D model of the town and art gallery, complete with source code.